Comparative analysis of the Mann reconstruction method for the problem of the interpretation of proxy data.

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Presentation transcript:

Comparative analysis of the Mann reconstruction method for the problem of the interpretation of proxy data.

The mathematical formulation of the problem The upscaling problem u = Az y = Sz + ν A  M m,n – the averaging operator S  M k,n – the separating operator The problem of interpretation of indirect measurements y = Gu +  G  M m,k – the observation operator

The Mann reconstruction method

Some frequently-used methods. (The case of one-dimensional predictand)

Locations of simulated data and psevo-proxies.

NH annual near-surface temperature. Reconstruction from using different methods.

NH annual near-surface temperature. Coefficient of efficiency for different methods.

NH annual near-surface temperature. Correlation coefficient for different methods.

NH annual near-surface temperature. Reconstruction from using different methods.

CalibrationVerificationMasked r(cal)r(ver)REr(cal)r(ver)RE SLR SLR(2band) MBH PLS ANN RR Grid-point Direct Southern European mean temperature. Comparison with predictand observations. Calibration period = Verification period =

Summary The Mann method comes from idea of the unbiased regression and thus seems to be acceptable for reconstruction of the low-frequency variability. In the one- dimensional case it makes right inflation of the regression with SVD decomposition and coincides with the inflated regression. It is also cheap from the computation point of view and seems to be robust to the increasing level of the white noise in proxy data. Probably the Mann method can lead to the big errors in the case when we have strong spatial correlations in the noise.